# CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

###### CAT Questions | Algebra | Progressions - Arithmetic Progression

The question is about a particular term of an Arithmetic Progression. It asks about 'x' times of the xth term. With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. CAT Exam tests the idea of progression often in the CAT Quantitative Aptitude section and this could also be tested in DI LR section of the CAT Exam as a part of a puzzle.

Question 7: If 4 times the 4th term of an A.P. is equal to 9 times the 9th term of the A.P., what is 13 times the 13th term of this A.P.?

1. 7 times the 13th term
2. 0
3. 13 times the 7th term
4. 4 times the 4th term + 9 times the 9th term

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### Video Explanation

Arithmetic Progression

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##### Method of solving this CAT Question from CAT Algebra - Progressions: The key is to frame the right equations.

4t4 = 9t9 , we need to find t13
4(a + 3d) = 9(a + 8d)
4a + 12d = 9a + 72d
=> 5a + 60d = 0
=> a + 12d = 0
=> t13 = 0
=> 13 * t13 = 0
As a simple rule, if n * tn = m * tm, then tm+n = 0. See, if you can prove this.

The question is "what is 13 times the 13th term of this A.P.?"

##### Hence the answer is "0"

Choice B is the correct answer.

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#### Other useful sources for Algebra Questions | Arithmetic Progressions Geometric Progressions Sample Questions

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